(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(+(x, 0)) → f(x)
+(x, +(y, z)) → +(+(x, y), z)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Precedence:
f1 > +2
0 > +2

Status:
f1: multiset
0: multiset
+2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

f(+(x, 0)) → f(x)
+(x, +(y, z)) → +(+(x, y), z)


(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE